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Sagot :
Answers:
- First car = 40 gallons
- Second car = 25 gallons
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Explanation:
I'll denote the cars with the labels A and B.
Car A has a fuel rating of 40 mpg (miles per gallon) and car B gets 20 mpg.
Let,
- x = number of gallons used by car A
- y = number of gallons used by car B
Since car A gets 40 mpg, and uses up x gallons, then it travels 40x miles. Multiply the fuel rating with the number of gallons used to determine the distance traveled. Car B travels 20y miles since it gets 20 mpg.
Overall, the two cars travel a combined distance of 40x+20y miles. This is set equal to the 2100 miles stated to form the equation 40x+20y = 2100.
Let's divided every term by 20
40x+20y = 2100
40x/20+20y/20 = 2100/20
2x+y = 105
Then isolate y to get
y = 105-2x
We'll use this equation later.
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The two cars use up a total of 65 gallons, which means,
x+y = 65
Then we'll plug in y = 105-2x and solve for x.
x+y = 65
x+105-2x = 65
-x+105 = 65
-x = 65-105
-x = -40
x = 40
Car A (the 40 mpg car) used 40 gallons. It traveled 40x = 40*40 = 1600 miles.
Car B (the 20 mpg car) used y = 105-2x = 105-2*40 = 25 gallons of gas. Or you could note that if x = 40, then x+y = 65 must lead to y = 25. It traveled 20y = 20*25 = 500 miles.
The two cars combined distance is 1600+500 = 2100 miles to help verify the answers.
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